The asymptotic stability of a nonstationary system with delay

In this paper we study the exponential stability of a linear system of differential equations with a constant delay such that the right-hand side of one of its subsystems contains an exponential multiplier. We establish sufficient conditions for the existence of an asymptotically periodic solution to the inhomogeneous system. © 2013 Allerton Press, Inc

Асимптотические свойства и стабилизация одной системы нейтрального типа с постоянным запаздыванием

The problem of obtaining sufficient conditions for the asymptotic stability for a certain class of linear systems of a neutral type with constant delay is analyzed in the article. Some coefficients of these systems in the right side have an exponential factor. As a consequence, the study of the stability of such systems with the help of the Lyapunov-Krasovskii functionals is not possible; methods of receiving asymptotic appreciations lead to extremely rough results. By applying the apparatus of difference systems and the properties of simpler systems, which the author examined previous, sufficient conditions for the exponential stability of such systems are obtained. As an example, a second-order system is considered. The graphs of the solutions of the corresponding system, both without neutral members and with the original system where the right-hand side contains neutral terms, are provided. On the basis of theory difference systems, the author proposes an algorithm of stabilization for some systems of a similar type. © 2021 Saint Petersburg State University. All rights reserved

Nature of quantum recurrences in coupled higher dimensional systems

We investigate recurrence phenomena in coupled two degrees of freedom systems. It is shown that an initial well localized wave packet displays recurrences even in the presence of coupling in these systems. We discuss the interdependence of these time scales namely, classical period and quantum revival time, and explain significance of initial conditions

Challenges in decomposing encodings of verification problems

Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence, we need techniques to make the solving process scale to large systems, such as partitioning (divide-and-conquer) and abstraction. In recent work, we showed how decomposing the formula encoding of a termination analysis can significantly increase efficiency. The analysis generates a sequence of logical formulas with existentially quantified predicates that are solved by a synthesis-based program analysis engine. However, decomposition introduces abstractions in addition to those required for finding the unknown predicates in the formula, and can hence deteriorate precision. We discuss the challenges associated with such decompositions and their interdependencies with the solving process

Stabilization of some systems with constant delay

An algorithm for stabilization of a class of systems with constant delay is proposed. © 201

Features of Muscle Tissue Microstructure of Cattle in Industrial Agglomerations under the Environmental Pressure Conditions

The intensive development of the industrial sector, intensification of the agro-industrial complex, associated with the use of various fertilizers, active use of modern household chemicals lead to the constant increase in xenobiotics in the environment in both rural and urban agglomerations. There are settlements and farms within the industrial areas, therefore, the issue of accumulation of ecotoxicants in the organs and tissues of an animal, as well as the impact on the state of its health, is of particular importance. In the regions with tough environmental situation associated with anthropogenic contamination, xenobiotics of anthropogenic origin can directly or indirectly modify the activity of various body systems. The integral characteristic that reflects adaptive modifications of biota is the morphological and functional status of organs and tissues of an animal, including the state of muscle tissue. An analysis of the regenerative plastic potential of muscle tissue allows finding innovative approaches to assessing the effects of environmental impacts on animals. Up to the present day, the morphological and functional characteristics of muscle tissue in young animals and adult cattle have not been sufficiently studied in the conditions of the tough environmental situation of the Central Federal District of the Russian Federation. The issue of ecological pathologies of organs in productive animals is quite urgent for the territory of the Central Federal District with its developed agro-industrial complex and industry. The study of animals from the agglomeration of the large chemical plant showed that cattle react differently to pollutants. The animals demonstrated changes not only in hematological and biochemical parameters, but also in the morphological and functional status of muscle tissue